First Advisor

Scott A. Wells

Date of Publication

Summer 8-2-2018

Document Type


Degree Name

Doctor of Philosophy (Ph.D.) in Civil & Environmental Engineering


Civil and Environmental Engineering




Hydrodynamics -- Mathematical models, Water quality -- Mathematical models



Physical Description

1 online resource (xix, 250 pages)


Numerical modeling has become a major tool for managing water quality in surface waterbodies such as rivers, lakes, reservoirs, and estuaries. Since the two-dimensional longitudinal/vertical model CE-QUAL-W2 is a well-known model and it has been applied to thousands of waterbodies around the world successfully, its numerical scheme was adapted to develop a new three-dimensional numerical model for simulating hydrodynamics, temperature, and water quality in surface waterbodies. Finite difference approximations were used to solve the fluid dynamic governing equations of continuity, free water surface, momentums, and mass transport. No coordinate transformations were performed and the z-coordinate system has been used. Higher-order schemes (QUICK, QUICKEST, and ULTIMATE QUICKEST) in addition to the UPWIND scheme were used for the advective temperature and mass transport. A novel numerical approach was used for the numerical formulation of the three-dimensional scheme. This approach forced the numerical solution of the free surface equation to be a tri-diagonal matrix form rather than a more computationally intensive penta-diagonal matrix solution. This new approach was done by linking a method called line-by-line with the free water surface numerical solution. Another new approach was that the three-dimensional numerical scheme involved a simultaneous solution of hydrodynamics, temperature, and water quality at every model time level instead of saving the hydrodynamic results to be used later for water quality simulation. Hence, this scheme allowed feedback between the hydrodynamics and water quality every time step. In addition, various unique numerical algorithms were employed from CE-QUAL-W2 such as the W2 turbulence model, selective withdrawal theory, surface heat fluxes, and water quality sources and sinks, making the three-dimensional model built on well-tested algorithms.

To test the model structure and assumptions, an analytical verification was performed by comparing model predictions to known analytical exact solutions test cases. Good agreement was showed by the model for all of these tests. A computation of the volume balance over the simulation period was also incorporated within the model to assess how well the code performed. Sensitivity tests were also made varying bed and wind shear.

The model was also applied to three reservoirs in the USA as field case studies: Lake Chaplain in WA, Laurance Lake in OR, and Cooper Creek Reservoir in OR. The model was validated by comparing the model predictions of water levels, velocities, vertical temperature profiles, and dissolved oxygen with field data. Through these real applications, the numerical predictions of the 3D model showed good agreement with field data based on error statistics. The model results of each field case study were discussed separately. In the Lake Chaplain model application, the study was focused on the importance of the higher-order schemes compared to the first-order UPWIND scheme. The model predictions of temperature were determined by using the UPWIND, QUICK, and QUICKEST scheme and compared with field data. The Error statistics of the model predictions compared to field data were an absolute mean error (AME) of 0.065 m for the water level predictions and an overall AME of 1.62 °C, 1.09 °C, and 1.23 °C for the temperature predictions by using the UPWIND, QUICK, and QUICKEST scheme, respectively. In the Laurance Lake model application, a comparison was performed between the present 3D model and the 2D CE-QUAL-W2. Since the 3D model was build based on CE-QUAL-W2, differences between the two models were evaluated. Error statistics between the model predictions of water level and temperature compared to field data showed that both models were in good agreement with field data. However, the 3D model AME (0.30 m for the water level predictions and 0.48 °C for the temperature predictions) was higher than the 2D model (0.03 m for the water level predictions and 0.42 °C for the temperature predictions). Finally, the Cooper Creek Reservoir case study was done to show the model predictions of temperature and dissolved oxygen. In this application, vertical temperature profiles were covered the entire simulation period in order to show how the model transfer heat between stratification and non- stratification conditions. The model showed good agreement with field data (0.12 m AME for the water level predictions, 1.00 °C overall AME for the temperature predictions, and 1.32 g/m3 overall AME for the dissolved oxygen predictions).

Finally, comparisons were made between CE-QUAL-W2 and the 3D model. The 2D model generally performed better in the tests cases if the model user is unconcerned about lateral impacts. The 3D model is important to use when lateral currents and variation in the lateral dimension are important.


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